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On the Cadlaguity of Random Measures

Robert J. Adler and Paul D. Feigin
The Annals of Probability
Vol. 12, No. 2 (May, 1984), pp. 615-630
Stable URL: http://www.jstor.org/stable/2243491
Page Count: 16
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On the Cadlaguity of Random Measures
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Abstract

We consider finitely additive random measures taking independent values on disjoint Borel sets in Rk, and ask when such measures, restricted to some subclass A of closed Borel sets, possess versions which are "right continuous with left limits", in an appropriate sense. The answer involves a delicate relationship between the "Levy measure" of the random measure and the size of A, as measured via an entropy condition. Examples involving stable measures, Dudley's class I(k, α, M) of sets in Rk with α-times differentiable boundaries, and convex sets are considered as special cases, and an example given to show what can go wrong when the entropy of A is too large.

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